A formula for the Jacobian of a genus one curve of arbitrary degree


Type
Article
Change log
Authors
Fisher, Tom 
Abstract

We extend the formulae of classical invariant theory for the Jacobian of a genus one curve of degree n <= 4 to curves of arbitrary degree. To do this, we associate to each genus one normal curve of degree n, an n x n alternating matrix of quadratic forms in n variables, that represents the invariant differential. We then exhibit the invariants we need as homogeneous polynomials of degrees 4 and 6 in the coefficients of the entries of this matrix.

Description
Keywords
elliptic curves, invariant theory, higher secant varieties
Journal Title
ALGEBRA & NUMBER THEORY
Conference Name
Journal ISSN
1937-0652
1944-7833
Volume Title
12
Publisher
Mathematical Sciences Publishers